SHALLOW WATER ACOUSTIC AMPLITUDE
FLUCTUATIONS AT 35 AND 65 KHz

Michael Thomas Korbet

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II

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onterey, California

SHALLOW WATER ACOUSTIC AMPLITUDE
FLUCTUATIONS AT 35 AND 65 KHz

by

Michael Thomas Korbet

Thesis Advisor:

W. Denner

March 197^

Approved Ion public KeJL&a&e.; dU>t>uhation anlimLtad.

T160860

Shallow Water Acoustic Amplitude Fluctuations
at 35 and 65 kHz

by

Michael Thomas JCorbet
Lieutenant, United States Navy
B.S., United States Naval Academy, 1966

Submitted in partial fulfillment of the
requirements for the degree of

MASTER OF SCIENCE IN OCEANOGRAPHY

from the

NAVAL POSTGRADUATE SCHOOL
March 1974

c /

ABSTRACT

An underwater acoustics experiment conducted in shallow
water (70 feet) off the New Zealand east coast in 1972-1973
is described. Short acoustic pulses of 35 and 65 kHz sound
were projected along near-orthogonal paths of approximately
300 yards. Environmental parameters were simultaneously
observed.

Statistical and spectral analyses of pulse heights were
performed on 12 selected runs using digital techniques.
Coefficients of variation ranged from 2.0% to 15.5%. In
almost all cases, higher variability was observed along the
acoustic path oriented perpendicular to the predominant
swell direction. Along this same path, periods corresponding
to common surface swell periods were frequently evident in
the autocorrelation functions of the fluctuations. Coherence
between the fluctuations along each path was low, averaging
about 0.1. Long period oscillations suggestive of modulation
by internal waves were apparent in several runs. No signif-
icant dependence of variability on acoustic frequency was
detected.

Microscale temperature fluctuations measured simultane-
ously are discussed.

TABLE OF CONTENTS

I. THE EXPERIMENT 8

A. BACKGROUND 8

B. OVERVIEW 12

C. PHYSICAL DESCRIPTION 13

D. DESCRIPTION OF SENSORS 21

1. General 21

2. Acoustic System 22

3. Temperature System 26

E. DATA ACQUISITION 27

II. DATA ANALYSIS 31

A. STRIP CHART RECORDING ■ 31

B. DIGITIZATION 31

C. CONVERSION 35

D. PULSE HEIGHT MEASUREMENT 35

E. SELECTION OF RUNS FOR DETAILED ANALYSIS 36

F. STATISTICAL ANALYSIS 39

G. SPECTRAL ANALYSIS 42

H. DISPLAY OF RESULTS 44

III. RESULTS OF ANALYSIS 45

A. TEMPERATURE FLUCTUATIONS 45

B. STATISTICAL RESULTS OF PULSE HEIGHT

ANALYSIS 46

C. SPECTRAL ANALYSIS RESULTS 48

D. DISCUSSION 52

IV. CRITIQUE OF EXPERIMENT 62

A. PARAMETERS 62

B. RUN LENGTH 63

C. RECORDING OF DATA 64

D. PHASE II RUNS 65

E. RELFECTED SIGNALS 66

F. LOG KEEPING 67

V. SUMMARY, RECOMMENDATIONS, AND CONCLUSIONS 68

APPENDIX A: PULSE HEIGHT TIME SERIES AND

ANALYSIS RESULTS 72

LIST OF REFERENCES 125

INITIAL DISTRIBUTION LIST 12 8

FORM DD 1473 130

LIST OF TABLES

I. Basic Data on Analyzed Runs 37

II. Sea and Weather Conditions During Each Run 38

III. Summary of Statistical Analysis Results 47

IV. Summary of Selected Results from

Spectral Analysis 49

LIST OF FIGURES

1. Map of Auckland-Leigh area in New Zealand 15

2. Map of experiment site near Leigh, New Zealand 16

3. Schematic of acoustic propagation equipment 23

4. a. Typical sample of microscale temperature
fluctuations and simultaneously observed
acoustic pulse heights 32

4.D. Expanded view of acoustic pulse sequence 32

5. Graph of coefficient of variation versus

number of bad pulses 53

6. Graph of bad pulses on Hydrophone 1 versus

those on Hydrophone 2 5^

7. Histogram from Pulse Height Analyzer for
pulses recorded during the 5 minute period
shown on temperature record: low thermal

activity 56

8. Histogram from Pulse Height Analyzer for
pulses recorded during the 5 minute period
shown on temperature record: high thermal

activity ■ 57

ACKNOWLEDGEMENTS

The author wishes to acknowledge the valuable guidance
and encouragement of Dr. Warren W. Denner from whom,
through countless hours of stimulating dialogue, I learned
the value of innovative and exploratory thinking. The
assistance and comments of Dr. Edward B. Thornton and Dr.
Robert H. Bourke are greatfully appreciated.

Particular note is due the Department of Physics of the
University of Auckland for the cooperation extended during
the conduct of the experiment. Special gratitude is offered
to the staff of the Naval Arctic Research Laboratory,
especially Mrs. Dorothy Underwood, for the gracious hospi-
tality and multiple resources made available during the
author's work at that facility.

The experimental research discussed in this thesis was
supported through contracts from the Naval Ordnance Systems
Command (Code 03C) .

I. THE EXPERIMENT

A. BACKGROUND

Acoustic fluctuations in the ocean first gained serious
attention as a result of sonar development and acoustic
experimentation during and immediately after World War II.
Variability in the pressure amplitude of an acoustic signal
received from a constant source was attributed to the
presence of moving inhomogeneities which continuously altered
the ray paths for energy to travel from the source to" the
receiver.

During this same time frame, the development of quick-
response thermopiles enabled Urick and Searfoss (1948, 19^9 )
to measure the micro-scale thermal structure of the ocean
near Key West, Florida. Recognizing the prominent role of
temperature in affecting the acoustic refractive index, they
proposed that the "thermal patches" evidenced in their
experiments were the cause of acoustic fluctuations.

Subsequent investigations — theoretical, laboratory, and
in situ — are summarized through 1964 by Urick (1967) • A
more detailed theoretical development and analysis can be
found in Skudryzk (1963).

Although a clearer understanding of the nature of the
ocean'.s fine structure is available now, compared to twenty-
five years ago, the equations often used to predict acoustic
variability are still those developed by Bergmann (1946) and
Mintzer (1953a, 1953b, 1954). Under the condition that

r << ka

-— where r = range from source to receiver,

k = acoustic wavenumber,

a = thermal microstructure scale length, i.e.,
the "patch size",

the acoustic variability, calculated as the coefficient of
variation, V, is given by:

*L Js U2r3 jJs

V " ( 15 * a3

where u is the RMS refractive index contrast of the

inhomogeneity .

2

At relatively long range, such that r >> ka , the

variability is given by:

„ _ t IT'S 2, 2 ,h
V = ( -75— y k ar)2

These two equations were derived under the assumption of
a Gaussian autocorrelation function for the temperature
fluctuations. The quantities V and u are calculated as:

V =

<(P -<P>)^>
(<P>)2

coefficient of variation; i.e., V is the
fractional standard deviation of the pressure
amplitude, P

V =

(1)

, where c = sound speed

= RMS variation of the refractive index.

The "patch size", a , is determined from the space auto-
correlation function of the temperature fluctuations as
measured by a sensor moving along a line through the tempera-
ture field. Invoking the hypothesis of "frozen turbulence,"
and allowing the temperature field to be advected past a
fixed sensor, • "patch size" can also be determined from the
temporal autocorrelation function of the temperature fluctu-
ations, <J>(t), where x is the lag time, provided the advection
velocity is known.

Mintzer (195*0 has shown that the autocorrelation func-
tion for the acoustic fluctuations, R(x), should be related
to the autocorrelation function for the temperature fluctu-
ations by the equation

<Kt) = R(x) .

Accepting Mintzer' s hypothesis, the temporal autocorrelation
function of the acoustic fluctuations should be identically
equal to that of the temperature fluctuations. One recent
experiment (Campanella and Favret 1969) which attempted to
verify this relationship found the above expression valid
under carefully controlled laboratory conditions.

Knowledge of the microstructure of the ocean has expanded
significantly In the past ten years. While the classical

10

concepts of thermal patches — spherical, spheroidal, or
lenticular — are still valid under some circumstances, they
have been largely overshadowed by the discovery of a layered
microstructure . Evidence of this type of structure has been
observed repeatedly in widely separated areas of the oceans
(Stommel and Federov 1967; Neshyba, Neal, and Denner 1971;
Woods and Wiley 1972; Neal and Neshyba 1973; Gregg, Cox, and
Hacker 1973, for example). However, the degree of structuring
and lateral extent of the laminae have been found to vary
considerably and unpredictably. Thus the tenant of local
isotropy and/or homogeneity is more difficult to support than
it is for the case of a patchy microstructure.

In conjunction with the investigation of a multi-layered
thermal microstructure, several theories have been proposed
to explain the mechanisms for the formation, maintenance,
and collapse of the fine structure. Briefly these include
internal waves (Garrett and Munk 1972), double diffusive
processes (Stommel and Federov 1967) , and billow turbulence
(Woods and Wiley 1972).

In addition to the thermal microstructure, whether it be
layered or patchy, other factors that cause acoustic fluctu-
ations may be present in the ocean environment. Among these
are microscopic bubble populations (Medwin 1973), micro- and
macro-biologic effects, and both surface and internal wave
activity (Crease 1963, Barakos 1972).

While many experiments have been performed to investigate
acoustic variability, few have simultaneously monitored the

11

essential features of the environment. Furthermore, few, if
any, measurements of acoustic variability have been made in
shallow water. The experiment described in this thesis was
designed to collect environmental and acoustic data which
would lead to an analysis of both temperature and acoustic
variability in a shallow water scenario.

B. OVERVIEW

The purpose of the experiment was to obtain simultaneous
measurements of both environmental data and acoustic data in
order to gain a better understanding of the nature of the
environment, to determine the driving forces evoking changes
in the environment, and to investigate the interaction
between the environment and acoustic propagation.

The environment under study was a shallow coastal region
with a mean water depth of approximately 70 feet. Several
advantages were immediately gained from the selection of
this site. The sensors involved could be rigidly fixed in
known positions on the ocean floor, thus eliminating the
problem of platform motion which is difficult to accomplish
in open ocean experiments conducted from research vessels.
However, the water depth was great enough to offer the oppor-
tunity to observe, as the seasons passed, both a well-mixed
(and therefore homogeneous and near-isotropic ) environment,
and a stratified environment. The extent of either situation
was determined by local wind, wave , and swell conditions.
Finally, the experiment was maintained for a period of

12

months in the same location; this allowed the accumulation
of sufficient data to form a long term time series.

During the course of the experiment, the following
parameters were to be observed and recorded:

1. high frequency acoustic amplitude fluctuations in
two simultaneous orthogonal directions

2. temperature microstructure data

3. mean water temperature

4. surface wave heights

5. velocity in two horizontal directions

6. vertical velocity

7. ambient noise

8. surface wind

9. stage of the tide

10. sky and cloud conditions

11. pertinent phenomena, such as sunrise, sunset,
precipitation, unusual occurrences, etc.

C. PHYSICAL DESCRIPTION

The site selected for the experiment was the University
of Auckland Marine Station at Leigh, New Zealand. Dr.
Denner of the Naval Postgraduate School was on sabbatical
leave with the Department of Physics of the University of
Auckland. The Physics Department at the University had been
active for several years in the area of acoustic fluctuations
in the ocean. Dr. Erick Sagar had contributed several
original papers in the area of sound amplitude fluctuations
(Sagar 1955, Sagar 1957, Sagar i960). Furthermore, the
university had previously conducted acoustic experiments at
Leigh (Brownlee 1969); hence, some of the necessary

13

facilities were already installed, namely, several conducting
cables and underwater instrument platforms. The Marine
Station provided the required logistic support including
laboratory space, boats, shops, personnel, etc.

The near-shore area where the range was established was
being set aside as a marine preserve and intrusions on the
range by fishing and recreational boats were eliminated.
The area was very biologically active, especially in plankton,
nekton, and algae populations (Morton and Chapman 1968,
Taylor 1972) .

Geographically, the Leigh Marine Laboratory is located
on the mainland across from Goat Island in the vicinity of
Leigh, approximately 40 miles north of Auckland on the east
coast of New Zealand (Figure 1). The range was located off-
shore from the laboratory between the mainland and Goat
Island (Figure 2).

The laboratory had served as a center of marine research
for a number of years and some of the environmental charac-
teristics of the area were known. In this regard, local
climatology was an important factor because the experiment
was planned to span a period of one year. Statistically,
the diurnal air temperature range was about 6°C in all seasons
of the year; this range was only slightly less than the mean
annual temperature change of about 10°C. The warmest month
was February v/ith an average daily temperature range of
20 to 2*)°C;the coldest month was August with a mean daily
range of 10 to 15°C. Sea surface temperatures historically

1H

175°E

Figure 1. Map of Auckland-Leigh area in Hew Zealand

15

16

varied from a low of about 13.5°C in August to a high of
about 20.4°C in February. In the winter the water column
was isothermal to the bottom. Warming of the water column
as summer approached resulted in slight thermal stratifica-
tion which reached a maximum in late October or November.
Due to the shallow depth at the range, temperature difference
between the surface and bottom waters was not expected to
exceed 2°C. No permanent thermocline existed and seasonal
thermoclines, if present at all, were weak. Surface salinity
values ranged from 3*1.20 to 35 . 86°^0 with a slight increase
with depth on the order of 0 .1 to 0.2%o between the surface
and 70 feet. Salinities tended to be slightly higher in the
winter and spring months, although this trend was not well-
established. Light to moderate winds were to be anticipated
for the majority of the time with speeds seldom exceeding
18 knots. Currents in the immediate vicinity of the experi-
ment site were irregular in direction and speed, the primary
contribution arising from tidal influence. Mean tidal range
varied from 5 feet during neap tides to 8 feet during spring
tides .

Geologically, the coasts currounding the site were
primarily greywacke and sedimentary type rocks. The rugged
coastal topography extended approximately 100 to 150 yards
offshore where it changed abruptly to a fairly level sandy
bottom upon which the instruments v/ere situated. The bottom
sediment was friable fine sand of mixed siliceous and
calcareous origin. High surface wave activity had the effect

17

of agitating the bottom sediments and distributing fine
particulate matter throughout the water column in a short
period of time.

The laboratory was the location of the majority of the
shore-based equipment. Twenty-one conducting cables from
the laboratory terminated at a secondary shelter, referred to
as the "Caboose," where they were joined to three seven-
conductor armored cables. The three armored cables were laid
over the coastal cliff and out to approximately 250 yards
offshore where a set of underwater junctions was located.
This site became known as the Bird Cage Site, an identity
referring to the metal protective cages in which the armored
cables were each joined to a four-conductor cable. Cables
of the latter type comprised the remainder of the range
wiring. One of the two hydrophones used in the acoustic
propagation portion of the experiment was placed at this
site atop a 20 foot mast; water depth was about 40 feet.

About 312 yards seaward from the Bird Cage Site was the
Tripod Site. A 20 foot high metal tripod had been erected
at this site as an instrument platform for a previous
experiment. The tripod became the main sensor platform for
this experiment. It was situated in approximately 80 feet
of water with an initial height of 20 feet above the bottom.
A 20 foot extension of PVC (Poly Vinyl Chloride) pipe was
added to the tripod to elevate the sensors to the center of
the water column. On the tripod mast were mounted the
acoustic projector, temperature and temperature microstructure

18

sensors, and ambient noise hydrophone. Approximately 100
feet seaward of the tripod, one Aanderaa current meter was
moored 20 feet above the sea floor.

In additon to the hydrophone placed at the Bird Cage,
a second receiving site was established at the base of an
underwater reef extending northeast from Goat Island
(Figure 2). Water depth at this location — the Reef Site —
was approximately 65 feet; the hydrophone was mounted atop
a *J0 foot mast secured to the sea floor.

By positioning the hydrophones in the manner described,
two near-orthogonal acoustic paths of approximately the same
length (actual path difference, determined acoustically, was
30 meters) were established. The Tripod-to-Bird Cage path
was oriented in the same direction as the predominant swell,
i.e., from the northeast to the southwest. Thus, the effects
of simultaneous acoustic propagation across-swell and along-
swell could be observed. Additionally, if the water were
stratified, the effect of internal waves could also be
observed if present.

A second Aanderaa current meter was moored 20 feet above
the bottom at a location approximately 100 feet east of the
Reef Site. The wave and tide sensor was situated in an
exposed area about 110 feet south of the Tripod Site.

All of the equipment and cables had to be installed by
divers operating from a 12 foot skiff. In addition to the
pre-existing cabling mentioned above, new cables had to be
installed from the Bird Cage Site to the Tripod, to the Reef

19

Site, and to the wave and tide sensor. These feeder cables
were terminated in either smaller, lighter cables that could
easily be brought to the surface for sensor connection, or
in underwater housings in which the instrument connection
was made .

Several significant problems were encountered in estab-
lishing the range. The small boat available required that
all of the equipment be relatively light. The use of divers
to install the equipment further dictated that size and
weight be limited to manageable dimensions. Virtually calm
weather was mandatory to insure a satisfactory installation.
Many of the sensors, particularly the thermistors, were very
fragile and required extreme care in handling.

Fouling and corrosion proved to be constant problems.
Experience showed that only a few days' data could be
obtained from the thermistors before they had to be cleaned
by a diver. Biological fouling grew at a rate of several
millimeters per week on exposed unprotected areas. Stainless
steel bolts available in New Zealand corroded through in only
a few weeks.

The occurrence of large waves, either locally generated
or swell from a distant storm, occasionally resulted in
damage to the underwater equipment. Such damage mainly
consisted of cable displacement and consequent stress or
failure of the junction terminals, thus necessitating
inspection and repair by divers.

20

D. DESCRIPTION OF SENSORS
1. General

At the- commencement of the experiment in September
1972, the following sensors had been installed:
Tripod Site:

1. mean temperature thermistor

2. temperature microstructure thermistor array

3. acoustic projector

k . ambient noise hydrophone

5. three components of ducted current meters

6. Aanderaa current meter moored about 100 feet
northeast of tripod

7. pressure sensitive wave and tide sensor located
about 110 feet south of the tripod

Reef Site:

1. hydrophone

2. Aanderaa current meter moored about 100 feet east of
the hydrophone mast

Bird Cage Site:

1. hydrophone

The horizontal components of the ducted current meters
failed within the first few days of operation. The remaining
vertical component operated successfully for the duration of
the experiment.

All sensors, with the exception of the Aanderaa
current meters, were hard-wired to the shore station for data
recording. The Aanderaa meters, which were Savonius rotor
type meters, digitally recorded current speed and direction
internally on magnetic tape for later retrieval.

21

In addition to the underwater measurements, meteoro-
logical observations were made by personnel at the Marine
Laboratory under a program separate from this experiment.
Standard atmospheric parameters, including air temperature,
dew point temperature, barometric pressure, wind velocity,
precipitation, and insolation, were monitored.

Two unique aspects of the sensor suite were the
acoustic and temperature components. Early in the preparation
for the experiment, two special problems were recognized.
The first was the requirement to measure temperature fluctua-
tions to an accuracy of at least t 0.01°C; the second was the
recording for analysis purposes of short ultrasonic pulses
received at two sites. Temperature was a problem because of
the sensitivity required over a large temperature range. The
acoustic pulses were a problem for two reasons: 1) the tape
recorder could not record directly the high frequencies used
without excessive tape usage, and 2) direct recording of the
received pulses would require an extremely fast digitizing
system if the data were to be analyzed on a digital computer.

Systems were designed to cope with these problems and
are described in the following sections.
2 . Acoustic System

A block diagram of the equipment involved in the
acoustic propagation portion of the experiment is shown in
Figure 3- Two Wavetek oscillators were used to initiate an
acoustic pulse at the desired frequency. The first oscillator,
which established the pulse repetition rate, triggered the

22

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second oscillator which produced the pulse. The second
oscillator, in turn, triggered the power amplifier and
simultaneously input the trigger signal to a specially
designed sample and hold circuit. The power amplifier drove
a horizontally omnidirectional projector at one of the two
experimental frequencies, 35 kHz or 65 kHz. The signals
from the hydrophones were passed via cabling back to the
shore station where they were input to the dual channel
sample and hold circuit .

This circuit, designed and constructed by personnel
of the Physics Department at the University of Auckland in
New Zealand (Ash 1972) operated as follows. The trigger
signal from the second oscillator initiated a sample inhibit
instruction in the sample and hold circuit to prevent the
circuit from being falsely triggered while the acoustic pulse
was traveling down range. The pulse output from the hydro-
phone preamplifier, approximately 2 volts peak-to-peak, was
amplified in the circuit to approximately 8 volts peak-to-
peak. By the time the pulse arrived at the circuit, the
sample inhibit signal had been cancelled. The first cycle
from the arriving pulse that exceeded a pre-set comparator
level enabled a 200 msec sample hold component. At this
point the peak-to-peak voltage value of the pulse cycle was
held for 200 msec. The 200 msec output signal was then
applied to a tape recorder. Approximately five cycles of
the pulse were required to initiate the sample and hold
process. After a pulse was Identified, the sampling circuit

2 'J

was disabled by a logic sub-circuit to avoid triggering of
the system by noise or reflections between direct path pulse
arrivals .

Pulse durations of 1.0, 1.5, and 2.0 msec were used
in various phases of the experiment. However, this did not
affect the operation of the sample and hold circuit since
pulse height was determined in the first five cycles of the
pulse train and later arrivals were ignored.

Pulse repetition rate as determined by the first
oscillator also varied, with nominal rates of 1 and 3 pulses
per second in use at different times. Problems associated
with the higher rate will be discussed in Chapter IV.

■The three transducers used in the experiment were
basically identical. Each transducer was comprised of a low
frequency and high frequency section, resonant to 35 kHz and
65 kHz respectively. The transducers were Model ITC601D
manufactured by the International Transducer Corporation of
Goleta, California.

Peripheral equipment consisted of an oscilloscope
which was used to monitor the performance of the sample and
hold circuit and to observe the degree of fluctuation
occurring during a run. In the latter stages of the experi-
ment, a pulse height analyzer was also placed in line to
obtain immediate analysis of height distributions.

Range geometry and water depths were such that
surface-reflected and bottom-reflected signals arrived at the
hydrophones sufficiently late enough to Insure that only

25

direct path measurements were made. During the initial
phase of the experiment, however, occasional interference
from surface-reflected arrivals did occur at the Bird Cage
Site under conditions of low tide and an acoustic frequency
of 35 kHz. A satisfactory solution to this problem was
obtained by lowering the mast at the site by 5 feet prior to
the commencement of later phases.
3. Temperature System

Glass encapsulated, fast response thermistors were
used for measurement of gross temperature and temperature
microstructure . For the gross temperature thermistor, the
Wheatstone bridge components were chosen so that the bridge
balanced at l4.5°C, the center of the anticipated temperature
range of 12°C to 17°C. A temperature range of this magnitude
was expected due to the long period of time planned for the
conduct of the experiment.

With the high resolution required for the micro-
structure measurements, a small change in gross temperature
would have quickly moved the microstructure bridge off
balance if a conventional Wheatstone bridge arrangement were
used. Thus, high resolution would have been available only
over a very limited temperature range. This problem was
overcome by using two equal resistors in the ratio arms of
the bridge and two matched thermistors in the opposite arms.
Thermal inertia added to one of the thermistors ensured that
only slow temperature changes were sensed. The other therm-
istor in the adjacent arm sensed both gross temperature and

26

temperature microstructure . Thus, the bridge output was
proportional to microscale temperature fluctuations but had
the ability to stay balanced over a wide range of gross
temperature. The stock of thermistors available was
calibrated in a bath from 11°C to 25°C and proved to be very
well matched and therefore suitable for this type of
arrangement .

For the microstructure measurements, a temperature
change of 0.1°C was set equivalent to a 1.0 volt change in
the bridge output; the microstructure thermistors were
essentially linear over a range of ± 0.1°C from the zero
point. The gross temperature range of 12°C to 17°C was
equivalent to a voltage output range of -2.0 volts to +2.0
volts with 0.0 volts registered at l4.5°C.

To make efficient use of the limited conducting
cables available, temperature data signals were frequency
multiplexed in the' underwater equipment and then transmitted
to the shore equipment in the laboratory where the signal was
demultiplexed by filters. The carrier frequencies for the
two signals were spaced sufficiently far apart to insure
that rejection of the unwanted signal by the filters was
effective .

E. DATA ACQUISITION

Preparation for the experiment began during the summer
of 1971. This included renovation of the Tripod Site and
underwater surveys to determine the best locations for

27

additional instrument masts and optimum routing to bring
the armored cables ashore. Placement of cables, masts, and
instruments was executed at various times through the summer
of 1972.

Phase I of the experiment with all sensors operating was
conducted during the period 26 September to 19 October 1972.
Following a six week break when alterations to the mast at
the Bird Cage Site were made, Phase II was executed in the
first two weeks of December 1972. Phase III of the experiment
took place during the first week of July 1973. The runs
analyzed in this thesis were all made during Phase I.

In order to establish a comprehensive data base, it was
planned to take measurements on an hourly basis and whenever
significant phenomena were observed. During Phase I, this
schedule was put into effect. However, data storage require-
ments dictated that the original schedule be modified to
acquisition of acoustic and environmental data four times
daily and during unusual occurrences (e.g., high swell, high
winds, abnormally calm sea, etc.). The four periods specified
were sunrise, midday, sunset, and midnight. This schedule
was maintained during the latter stages of Phase I and during
Phase II. The schedule for Phase III was further modified
to provide for as near-continuous data collection as possible
during the two days that spanned this phase.

Because of the expansive data accumulation anticipated,
run length during Phases I and II was planned to be nominally
10 minutes. It was calculated that a run of this relatively

28

short length would be long enough to satisfy the requirements
for statistical and spectral analysis of the fluctuations in
the temperature and acoustic data. On occasions when extreme
variability was observed, run length was extended to twenty
minutes. During Phase III, run length was arbitrary, with
the shortest run being 27 minutes and the longest 77 minutes.

In order to investigate the frequency dependence of the
acoustic fluctuations, runs were generally conducted in
series of two, alternating the high and low frequencies in
each series. Due to the mechanical manipulations required
to change frequency, the two runs in a series were separated
by a period of about 8 to 20 minutes.

Two magnetic tape recorders were in use during Phases I
and II of the experiment. One was a four channel Hewlett-
Packard Model 3960, with a tape capacity of 1800 feet of
1.5 mil tape; the second was a seven channel Ampex FR1300
model with a capacity of 2500 feet of 1.5 mil tape. On the
Ampex tapes mean temperature, temperature microstructure,
pulse heights from both hydrophones, and the current data
from the three ducted current meters were recorded. Wave
height data, turbulent velocity data from the vertical compo-
nent ducted current meter, multiplexed temperature data, and
pulse height data on a time-sharing basis were recorded on
the Hewlett-Packard recorder. The first half of a run was
dedicated to Hydrophone 1 at the Bird Cage Site, and the
second half to Hydrophone 2 at the Reef Site.

29

Aanderaa current meter tapes were processed after
retrieval by displaying the data on a calibrated strip
chart. Except for a few runs in Phase II, ambient noise
was not recorded, but was monitored during each run. Also
in use was a four channel strip chart recorder which dis-
played wave and tide information, gross temperature, and
temperature microstructure data on a real time basis.

Log-keeping involved recording of dates, times, tape
recorder channel allocations, significant wave height (H ,_)
stage of the tide, and a summary of weather conditions.
Wave height and tide information were determined to the
nearest 0.1 foot from the strip chart.

Because the experiment was a joint venture between
personnel from the University of Auckland and from the Naval
Postgraduate School, copying of data tapes was required
after each phase to make the data available to both parties.
Selected tapes from the Ampex and Hewlett-Packard recordings
were transcribed onto one inch, fourteen track magnetic
tapes with the use of a Sangamo 3562 tape recorder. Addi-
tionally, copies of the experiment logs and of some of the
current and wave strip charts were returned to the United
States for analysis.

During Phase III, the Sangamo recorder was used for
initial data acquisition and dubbed tapes were provided to
the University of Auckland.

30

II. DATA ANALYSIS

A. STRIP CHART RECORDING

The first step in the analysis procedure was to survey
the transcribed data to determine qualitatively the nature
of the experimental runs available. Initially, this was
attempted by viewing the data on a dual-trace oscilloscope.
However, only two channels could be viewed simultaneously
and no permanent visible record was produced.

The magnetic data tapes were then played back on the
Sangamo tape recorder with the output displayed on an eight
channel Brush strip-chart recorder. The two tape channels
containing hydrophone information were input directly to the
Brush recorder. Each channel containing temperature data
was first low pass filtered through a Krohn-Hite Model 33^0
filter at 20 Hz to eliminate high frequency noise that may
have contaminated the signal. The filtered data were then
displayed on the Brush recorder chart.

A typical section of pulse height data and temperature
microstructure data is shown in Figure 4(a). Figure 4(b)
shows an expanded view of a typical pulse sequence.

B. DIGITIZATION

After screening the data for noise and run length, thirty-
five runs made during the period 30 September through 13
October 1972, and five runs from the period 2 through 3 July
1973 were selected to be digitized. None of the runs from

31

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Phase II of the experiment were chosen. Pour channels of
acoustic and temperature data were digitized. Digitization
was accomplished through the use of a COMCOR 5000 analog
computer, a Scientific Data Systems XDS 9300 digital computer,
and a Naval Postgraduate School analog-to-digital conversion
program. All of the above were available in the Electrical
Engineering Computer Laboratory of the Naval Postgraduate
School .

In the digitization process, the most critical factor to
be specified was the sampling rate. Based on a requirement
to accurately define the pulse height on the digitized
record, a sampling rate equivalent to 256 samples per
channel per digital record was selected. This rate translated
to a sampling time increment of 0.04 seconds between samples.
Since the length of a pulse was 200 msec (0.2 seconds), the
sampling rate insured a minimum of five samples on a normal
pulse height and a maximum of six samples if the first sample
on the pulse happened to occur exactly at the leading edge.
Each hydrophone channel was input directly from the Sangamo
tape recorder to the analog patchboard where the signal was
amplified 25 times.

The Nyquist frequency associated with the sampling rate
was given by the equation,

f = 1

c 2At
where At = sampling time increment.

33

For the increment chosen, 0.04 sec, the Nyquist frequency
was 12.5 Hz. This frequency was above the highest frequency
of significant fluctuations expected in the temperature
microstructure data and was high enough to minimize aliasing.

Temperature data were played into the input of the analog
patchboard where a plus 10 gain was applied. The amplified
signal was then low pass filtered at 50 Hz to eliminate
locally generated 60 Hz noise that was apparent in initial
trial runs. Because tape playback during digitization was
conducted at 16 times real time, the actual temperature data
was, in effect, filtered at 3.125 Hz. The filtered signal
was then input to the patchboard where a second plus 10 gain
was applied. Total amplification of the temperature data
was 100 times. Of several methods evaluated for filtering
and amplifying the temperature data, the above method
appeared to be the most practical and efficient in eliminating
the locally introduced 60 Hz signal.

In addition to the above procedures, biasing- of the
amplified signal was required to keep the signal voltage
within the ± 100 volt range of the analog computer. The
COMCOR 5000 provided bias adjust on each channel.

Each analog run was converted to a digital file of
discrete samples. These samples were written on seven track
magnetic tape in octal base notation. Each file contained
all four channels of digitized data applicable to that run.
Data in a file were written in blocks of 1024 samples called
digital records; each record spanned 10.24 seconds of real
time data.

3'J

C. CONVERSION

Continued analysis was to be performed on the IBM 360/67
digital computer at the Naval Postgraduate School. However,
it was first necesary to make the digitized data compatible
with the IBM 360 system. The conversion process involved
changing the notation from octal base to hexadecimal base,
and rewriting the data on a nine track magnetic tape. The
conversion was made using programs available at the Naval
Postgraduate School computer center and described in a
current technical note (Raney 1973) .

D. PULSE HEIGHT EXTRACTION

Of the 256 samples per channel in one digital record
which represented 10. 24 seconds of data, only about 50 of
the acoustic channel samples actually fell on a pulse height
peak. Furthermore, these 50 samples accounted for only 10
pulses. In order to conserve core storage, it was necessary
to compute and store only the pulse height value, rather than
read into memory an entire file, consisting of an average
58 digital records.

A program was written to read from the tape only the two
channels containing pulse data. When one digital record had
been read in, the pulse heights for each acoustic data channel
were computed and stored. Upon completion, the next suc-
ceeding record was read from the tape and processed. This
sequence was continued until the entire file had been
analyzed.

35

Programming precautions were taken to insure that no
pulse heights were missed on either channel and that only
actual pulse heights were retained; i.e., spurious noise
spikes were omitted.

E. SELECTION OF RUNS FOR DETAILED ANALYSIS

Of the 35 runs in Phase I that were digitized, three were
unacceptable due to excessive random noise that was apparently
acquired during digitizing. From the remaining 32 runs,
twelve were selected for detailed analysis. The selection
criteria were to form a suite of runs that were representative
of all typical environmental conditions, and to choose runs
that for one reason or another (e.g., frequency, time of day,
time sequence) were suitable for comparison with each other.

No runs from Phase III were considered due to low apparent
variability and difficulty with the data resulting from
unexplained interchannel feedback somewhere in the data
acquisition stage.

Pertinent details of the twelve analysis files are shown
in Table I. Because of digitizing requirements, the file
length was always slightly shorter than the actual experiment
run length. Table II summarizes the environmental conditions
present during each run. The comments section of Table II
was synopsized from the original logs kept during the
experiment .

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38

P. STATISTICAL ANALYSIS

In order to perform the planned spectral analysis, an
accurate determination of the pulse repetition period was
required. To obtain this, the average time increment, At,
between pulses (Table I) was computed. This increment was
the measure of the frequency with which an acoustic pulse
"sampled" the medium.

The time increment, At, was found by computing the total
time elapsed between the first sample on the first pulse in
a run, and the first sample on the last pulse in the same
run. This elapsed time, referred to as file length in
Table I, was then divided by one less than the total number
of pulse heights.

The analog-to-digital sampling period of 0.0*1 seconds
was the maximum error possible between the actual analog
file length and the digital file length as computed above.
Thus, for a file having a nominal 601 pulses (see Table I),
the maximum possible error in the computed average pulse time
increment, At, was on the order of:

(At) = - •°!ln^ec = ± 6.7 xlO"5 seconds
max 600

error

An error of this magnitude was considered acceptable for the
precision required to perform a valid spectral analysis of
the pu]se heights.

39

Computation of certain statistical parameters was the
next step in the analysis scheme. A pre-compiled subroutine
available in the Naval Postgraduate School IBM 360 library
was used to compute the coefficient of variation, the
minimum and maximum values and the range of the distribution.
The pulse height histogram was also computed and plotted.

It was immediately apparent from the histograms that a
small percentage of pulses had either extremely high values
or low values. However, this result was expected from the
Brush recordings which showed a random occurrence of
"drop-outs" and "spikes". The origin of these anomalies was
not exactly known, but it was apparent that they did not
represent real acoustic fluctuations. To eliminate these
a program was written to filter the pulse heights through a
gate whose width could be varied. The acceptable gate width
was determined by a trial and error process. The method
employed in this smoothing process was to compare a pulse
height with a running mean computed from the previous ten
pulses. The first ten pulses In a file were tested against
the mean of the first twenty heights to initiate the process,
The gate was centered around the mean. A bad value was
eliminated by substituting an artificial pulse whose height
was determined from a linear interpolation between the
preceding good pulse and the next succeeding good pulse.
Pulse heights filtered in each computer run were compared
with the Brush chart to determine if any good data had been
filtered or if any anomalies had been missed. This method

HO

did not eliminate all bad pulses and on some runs one or
two erroneous pulses escaped correction. Since these few
represented a very small percentage of the total sample —
less than 0.5$ — no further attempts were made to smooth
them. Thus the temporal fluctuations in the smoothed
distribution were, with rare exception, the result of actual
acoustic variability.

The smoothed data were then re-analyzed as discussed
above. Of all the basic statistics computed, the coefficient
of variation was the most pertinent. Skewness and kurtosis,
which were computed along with other statistics, would have
been valuable for comparison of histograms but were
invalidated for this purpose because the class interval
varied among distributions. In computing the histograms,
the constant factor was the number of class intervals rather
than the width of the class interval; this feature was a set
characteristic of the subroutine.

To facilitate comparison of results among runs, the
pulse heights of each run were normalized to the mean for
that run. Each pulse height sequence, then, had a mean of
1.0, and each pulse value was expressed as a percentage of
the mean. This process had no mathematical effect on the
coefficient of variation. Conversion of pulse heights to
standard variables was also done so that distribution in
terms of standard deviations was available.

Hi

G. SPECTRAL ANALYSIS

Following procedures detailed in Bendat and Piersol
(1966), preparation of the pulse height time series for
spectral analysis started with removal of the mean and of
any linear trend present in the series.

An estimate of the autocorrelation function, R(t), for
each time series was computed using the formula:

, N-m

R(t) = ± E (X)(X x )
N , n n+m
n=l

where N = the number of time samples, i.e., the
number of pulses in each run
m = the lag number
t = the lag time = m(At)
X = the individual pulse height value

The values for t were incremented from t=0 to a maximum lag
value of approximately one-tenth of the file length. The
increment used was the At determined by the method in
Section II. F.

A Parzen lag weighting function was then applied to the
autocorrelation function in order to insure a better estimate
of the spectral energy density values.

The autocorrelation function was Fourier transformed to
arrive at an estimate for the spectral energy density
function, G(f). The digital programming was derived from
the integral expression:

H2

G(f) = K I R(x) cos 2TTfT dx
0

where R(t) = the autocorrelation function
f = frequency
x = lag time

Estimates were computed for narrow frequency bands over the

range from D.C. to f where f is the Nyquist frequency

applicable to each run.

The cross correlation function R (x) between Hydrophone

xy

1 and Hydrophone 2 was computed next, using the equation:

n N-m

Rxy(T) = N=m" \ XnYn+m
n=l

where X = pulse height value for Hydrophone 1
Y = pulse height value for Hydrophone 2
and N, m, and x were as previously defined.

As with the autocorrelation functions, a Parzen window
was used to smooth the cross correlation function prior to
computation of the cross-spectral energy density function.

The co-spectral density and quadrature spectral density

2
functions were used to obtain the coherence, y , and

phase, 0 , functions for the pulse height time series:

2/ % c 2(f) + Qxy2(f)

xy G (f) G (f)
xv y

'13

-1 Qxv(f)

6 (f) = tan 1 SL

xy c (f)

xyv

2

where y (f) = coherence between Hydrophone 1 and
xy

Hydrophone 2 as a function of frequency

6YV(f) = phase between Hydrophone 1 and
xy

Hydrophone 2
C (f) = co-spectral energy density function
Q (f) = quadrature spectral energy density
function
G (f) = spectral energy density function for

Hydrophone 1
G (f) = spectral energy density function for
Hydrophone 2 .

H. DISPLAY OF RESULTS

The following computer generated plots were made on the
CALCOMP plotter:

1. relative pulse height time series for each hydrophone

2. autocorrelation functions for each hydrophone

3. auto-spectral energy density of the acoustic
fluctuations for each hydrophone

!\ . phase and coherence between Hydrophone 1 and 2 .

Except for one instance (Run 73) where the file length
was longer than usual, all runs were plotted using identical
scaling factors.

i\H

III. RESULTS OF ANALYSIS

A. TEMPERATURE FLUCTUATIONS

Detailed analysis of the temperature micro-structure data
was not performed in the course of this thesis. However,
the Brush chart recordings previously described afforded an
opportunity for a* qualitative evaluation of the micro-
structure activity present during each run. Of the twelve
runs under discussion, four showed temperature fluctuations
that were considerably more active than the others. The
remainder of the runs occurred under temperature conditions
varying from negligible to moderate activity. The most
active runs were numbers 72, 73, 116, and 117. Representative
samples of the twelve temperature records are shown in
Appendix A.

The temperature microstructure fluctuations were
evaluated using the thermistor calibration factors, tape
recorder gains, and the gain and chart speed settings for
the Brush recorder. An arbitrary classification scheme was
employed to assign qualitative descriptors:

Temperature Fluctuation Classification

< 0.05°C Negligible

.05°C to 0.2°C Moderate

> 0.2°C High

'15

B. STATISTICAL RESULTS OF PULSE HEIGHT ANALYSIS

Table III summarizes the statistical results obtained
from the analysis. Reference to Tables I and II supplies
information relating the acoustic frequency, time of day,
and environmental conditions to these results.

The coefficients of variation ranged from a low of 2.03$
(Run 56) to a high of 15.53% (Run 116) . The five highest
coefficients occurred in runs of relatively high thermal
activity. In general, the variation observed on Hydrophone 2
was slightly higher than that on Hydrophone 1, the exceptions
being Runs 45, 46, and 72. However, in only four runs (60,
73 » 116, 117) was the difference between the two hydrophones
greater than 2%; three of these four runs were also classified
as having higher microstructure content than the others.

Significant differences between the high frequency runs
and low frequency runs were more difficult to determine. For
runs that were conducted in high and low frequency pairs (see
Table I), the coefficients of variation for both Hydrophone
1 and 2 during the high frequency run were generally slightly
higher than during the low frequency run. However, since
the two runs in a pair were conducted 8 to 2*1 minutes apart
(Table I), the difference may not have been due to frequency
change alone.

Table III also has two sections pertaining to the range
of the distributions of pulse heights. The first of these
sections lists the extremes of the distribution in terms
of standard deviation. The second shows the range in terms

16

in % Relative to Mean
Maximum Range

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17

of percentage deviation from the mean. Information about
the shape of the distribution can be inferred from these
statistics. A relatively large c range coupled with a rela-
tively small percentage deviation indicates that the dis-
tribution is closely packed about the mean; this is reflected
in a low coefficient of variation. The converse situation
implies a relatively flat, dispersed distribution with a
consequently higher coefficient of variation. The coeffi-
cient of variation can be obtained by computing the ratio
of relative percentage range to standard deviation range .
However, the defining equation given in Chapter I was used
to calculate the coefficients given in Table III.

C. SPECTRAL ANALYSIS RESULTS

Computer generated plots for the twelve analyzed runs
are presented in Appendix A. Each series of four plots for
each run contains the time series of pulse heights plotted
relative to the mean, the autocorrelation functions for
each time series, the auto-spectral energy density functions,
and the coherence and phase functions determined from the
cross-spectral analysis between Hydrophones 1 and 2.

Table IV summarizes the lag times determined for three
values of the autocorrelation function (0.5, e , and 0.0),
approximate values of strong periodicities observed in the
autocorrelation functions, and the maximum value of coherence
attained between the two hydrophones.

'if;

Run Hydro-
. Number phone

Autocorrelation Lag Times
(sec)
Ve

l0.5

0.0

Apparent Maximum
Periodicity Coherence

45
46
48
49
56
58
60
61
72
73
116

117

1
2

1
2

1
2

1
2

1
2

1
2

1
2

1
2

1
2

1
2

1
2

1
2

5.5
2.0

7.4
1.2

1.1
11.1

13-9
5.3

0.8

1.2

0.9
1.7

4.8
1.1

0.8
1.1

12.6

3.1

10.9

1.3
2.7

1.5
2.8

8.1
2.5

9.8
2.0

4.0
17.6

17.3
11.1

1.8

1.6

1.9
2.1

16.3
7.7

1.7
1.8

15.5

6.5
17-6

1.7
25.2

1.9
41.9

17.1
33.3

28.8
19.8

19.3

28.8
29.8

11.1
3.2

19.2
11.0

20.1
3.5

26.7
31.3

24.2
40.4

None
None

None
8 sec

None
None

None
None

None
8 sec

None
None

None
7 sec

6 sec
6 sec

None
None

None
None

4 sec
7.5 sec

7.7 sec
6 . 5 sec

0.21

0.34

0.20

0.28

0.23

0.21

0.21

0.19

0.18

0.43

0.29

0.22

Table IV. Summary of Selected Results
From Spectral Analysis

49

The autocorrelation functions exhibited a wide variety
of characteristics which were related to the acoustic fluc-
tuations, and consequently to the state of the medium at
the time the run was conducted. In a run when the temperature
microstructure activity was low to moderate, evidenced by
the figures in Appendix A, and the wave activity was low
(Table II), the two autocorrelation functions were roughly
comparable. For runs that occurred in pairs (Table I),
no reliable trend was detected to indicate significant
difference due to a change in acoustic frequency. When
periodicities were apparent in the autocorrelation functions,
they were stronger on Hydrophone 2 than on Hydrophone 1.
Runs 72 and 73, conducted two hours apart during periods of
relatively high thermal activity, did not evidence any
strong periodicity, unlike Runs 116 and 117, conducted under
apparently similar thermal conditions. Significant wave
heights for these two sets of runs were 0.6 feet and 1.8
feet, respectively. For runs where the autocorrelation
function showed a marked periodicity, a distinct peak in
the spectral energy density was evident. However, many of
the peaks in the energy spectrum were not manifested in
readily definable periodicities in the autocorrelation
function .

All but two autocorrelation functions exhibited a definite
trend towards zero with increasing lag time . Hydrophone 1
for Run 72 was decaying very slowly, but had not reached

50

a value of 0.5 at the maximum time lag of 55 seconds. In
Run 49, Hydrophone 1 decayed continuously from t = 0,
crossing the zero axis at 30 seconds and continued to decay
until it exceeded the scale capability of the plot at a
value of -0.34 and t = 43.2 seconds. However, the computer
printout showed that the autocorrelation function reached
a minimum of -O.38 at 51 seconds and was increasing towards
zero at the maximum lag time of 58 seconds.

For all runs, the coherence between Hydrophones 1 and 2
was very low with an average value on the order of 0.1.
The maximum coherence listed in Table III occurred on a
coherence peak that was not representative of the entire
run. A maximum coherence of 1.0 would have indicated a
linear relationship between the fluctuations on Hydrophone
1 and those on Hydrophone 2; conversely, a coherence function
of 0.0 would have meant that the fluctuations were unrelated.
For intermediate values, three possible situations could
have existed [Bendat and Piersol 1966]:

1. extraneous noise was present in the measurements

2. the relationship between the fluctuations on each
hydrophone was non-linear

3. the fluctuations on one hydrophone were not driven
entirely by the same mechanisms as the fluctuations
on the other hydrophone

With consideration of the experimental parameters, a non-
linear relationship between the fluctuations was the most
plausible reason for the low coherence.

The phase function for all runs Is very erratic, a
further indication that a simple linear relationship did
not exist between the two hydrophones.

D. DISCUSSION

The success of the analysis of the acoustic data was
predicated on the reliability of the sample-and-hold circuit
described in Section I.D.2. Therefore, due scrutiny was
given to the number of bad pulse heights that were detected
by the smoothing process outline in Section II. F. If the
number of bad pulses were proportional to the acoustic
variability, the probability that such pulses may have been
actual acoustic fluctuations is increased. Plotting the
coefficient of variation versus the number of bad pulses,
Figure 5, did not support a relationship between the two
parameters. Data for Figure 5 were taken from Table III
and all points were plotted except those for Run 73 which
was twice as long as any other run.

The number of bad pulses, however, did seem to be related
to frequency. There were significantly more rejected pulses
at 65 kHz than at 35 kHz. This suggested that the sample
and hold circuit was encountering trouble in "following"
the 65 kHz wave form. However, Hydrophone 2 showed 2 to
3 times more bad pulses than Hydrophone 1. A plot of the
number of bad pulses that occurred on Hydrophone 1 against
the number on Hydrophone 2 for both frequencies, Figure 6,
indicated a strong relationship between the two parameters.

52

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Since the hydrophones were identical and operated well
throughout the experiment, the bad pulses could only have
been generated in the two channels of the sample and hold
apparatus. The critical question was: Did the malfunction
nullify the experiment? Evidence to the contrary was ex-
plicit in the pulse height histograms which clearly showed
the bad pulses separated from either side of the main
grouping. Furthermore, the Brush chart time series supported
the conclusion that, except for the random occurrence of
a bad pulse, the sample and hold circuit performed reliably
on all other pulses .

During Phase II of the experiment, an on-line Pulse
Height Analyzer was installed to obtain a real-time analog
display of pulse height distributions. Sample histograms
from two runs made under conditions of low and high micro-
structure activity are shown in Figures 7 and 8 . The Pulse
Height Analyzer was storage limited to the number of pulses
in a five minute segment of the run. The corresponding five
minute portion of the temperature microstructure record is
shown for comparison. The histograms obtained by digital
methods in this thesis were comparable to the distributions
accumulated by the Pulse Height Analyzer. This promoted
additional confidence in the sample and hold electronics.

A's noted previously, the degree of thermal activity
varied considerably during the runs from Phase I that were
analyzed. Runs 72, 73, 116, and 117, all conducted under
conditions of similar temperature fluctuations, exhibited

55

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57

notable differences in acoustic variability. Referring to
Tables I and II, Runs 72 and 73 were made under conditions of
very light wind and a virtually calm sea surface over the
acoustic range. The runs conducted the previous day (Runs
56-61) also experienced calm weather. From the logs, the
conditions on 2 October prior to Run 72 were similar with
calm winds and sea and a high, thin broken to overcast sky.
The large acoustic fluctuations observed during Runs 72
and 73 were indicative of the microstructure activity. No
strong periodicities were apparent in the- autocorrelation
functions and the spectral energy density functions for both
hydrophones during each run were similar.

In contrast, the weather and sea conditions (Table II)
were different during Runs 116 and 117. The acoustic, as
well as temperature, fluctuations were large, similar to the
runs on 2 October. However, the autocorrelation functions
exhibited marked periodicities and the spectral energy
density functions had a distinct peak at about 0.14 Hz.

Although the comparison is made between two sets of runs
conducted eleven days apart, one conclusion appears reason-
able. The acoustic fluctuations were induced by at least
two mechanisms in the medium, the temperature inhomogeneities
and the effect of surface wave activity. This situation has
been observed in other experiments as well [Alexander 1972,
for example]. Confirmation of the effect of surface waves
would require an analysis of the wave spectrum, the data for
which were not available for this study. However, the periods

58

seen in the autocorrelation function (Table IV) are readily
observed in a surface wave spectrum. A sample calculation
of the water particle velocity at a depth of 20 feet indicated
that the velocity effects should have been small for the
wave heights present. However, the presence of waves can
affect the transmitted acoustic energy in the wave spectrum
if inhomogeneities are present, viz., temperature and salini-
ty contrasts, bubbles, biologies. Then the wave induced
particle motion would serve to move these inhomogeneities
in and out of the propagation path in a periodic manner.

The pulse height time series for Runs 116 and 117 also
presented evidence of long period fluctuations upon which
the higher frequency excursions were imposed. The oscilla-
tion was distinct on the records for Hydrophone 2, but
barely discernible on Hydrophone 1. Run length was too
short to define this fluctuation in the spectral analysis,
although its effect was evident in the autocorrelation
functions for Hydrophone 2. The high coefficients of
variation for Hydrophone 2 In Runs 116 and 117 were caused
by the non-stationarity of the mean associated with this
fluctuation. If the coefficients for these two runs are
discounted, the variation for the set of 12 runs analyzed
then ranged from 2% to 10$. The apparent period, greater
than five minutes, and its occurrence in two runs conducted
eighteen minutes apart indicated the possibility of the
presence of Internal waves. Climatology, discussed in
Section I.C., showed a trend for thermal stratification to

59

occur in October as the summer months approach, thus pro-
viding the requisite density interface for internal waves.
Other runs, particularly 60, 72 and 73, showed indications
of long period fluctuations, but not as distinctly as Runs
116 and 117. Analysis of the temperature microstructure
data would not be conclusive in evaluating the internal
wave hypothesis because of the short run length compared
to the period of fluctuation. A similar situation was
reported by Shoemaker (1971) in the Arctic.

The definite appearance of this "wave" on Hydrophone 2
and its simultaneous absence from Hydrophone 1 were suppor-
tive of the anisotropy of the range . Further evidence of
a direction dependence was apparent in the time series plots
of pulse heights and in differences in the autocorrelation
functions for other runs, notably those runs where a marked
periodicity occurred (Table IV). In those cases, Hydrophone
2 always exhibited a stronger periodicity than Hydrophone
1. In all but three runs (45, 46, 48), the total spectral
energy, derived from computing the area under the spectral
energy density curves, was greater for Hydrophone 2. The
apparent cause of the difference in acoustic fluctuations
along the two orthogonal paths was the influence of surface
waves .

In addition to the possible causes discussed above -
temperature inhomogeneities , internal waves, and turbulent
water particle velocity - other factors that may have
Influenced the acoustic propagation were bubbles, sediment

60

particulate stirred into the water column, and biological
activity, not the least of which were the whales observed
during Run 58.

61

IV. CRITIQUE OF EXPERIMENT

A. PARAMETERS

Data on several additional parameters would have aided
in the analysis of the acoustic data. The first of these
was vertical temperature profile information. No profiles
were available to determine the presence or confirm the
absence of seasonal or diurnal thermoclines during the runs.
Such information could only be weakly inferred from clima-
tology and current and past weather data pertinent to each
run. A temperature profiling system was designed and built
but technical problems and lack of conductors precluded its
operation. The requirement for a remotely controlled system
which would operate reliably from a known, fixed location
under a variety of sea state and temperature regimes was
not attainable in the time frame of the experiment. The
other alternative was to take bathythermographs from a
vessel stationed on the range during each run, but the
instrumentation was not available.

Turbulent velocities measured by the ducted current
meters were limited to the vertical direction after the
failure of the horizontal components in the initial stage
of the experiment . Although the remaining component was
recorded, it was not recoverable from the magnetic tape.
The reason for this malfunction was the failure of the
microswitches , which could not be replaced during the

62

experiment. Availability of the vertical velocity data
would have enabled a cross-correlation investigation of
the effects of particle velocity on the acoustic fluctuations,
although time for this analysis may not have been available.

The current records from the Aanderaa current meters
are being analyzed in New Zealand and the data corresponding
to the runs analyzed herein were not available during this
effort. Hence no information concerning advective processes
affecting the range could be determined.

Surface wave data were restricted to significant wave
height as recorded on the logs. Data on wave periods present
during a run would have aided the analysis of periodicities
in the autocorrelation functions.

As detailed in Section I.B., the purpose of the experi-
ment was to investigate both the acoustic fluctuations and
the microscale features of the medium. It is felt that the
parameters listed above would have been useful in an analysis
of the temperature microstructure as well as of the acoustic
propagation. With regard to temperature analysis, a measure
of insolation more quantitative than logged comments about
sky conditions would have been advantageous .

B. RUN LENGTH

In Phase I, run length was nominally ten minutes. By
using a maximum time-lag of one-tenth the run length, periods
ranging from D.C. to about 55 seconds were able to be detec-
ted with reasonable definition in the autocorrelation and

63

spectral energy density functions. Better resolution could
have been obtained with the same number of lags by decreasing
the maximum lag time or increasing the run length. Decreas-
ing the maximum lag time has the effect of shortening the
longest resolvable period with the same number of lags.
Thus j maximum lag was selected as large as possible to take
advantage of the entire run length as a fixed parameter.

During Phase II, run length was increased to twenty
minutes to enable the detection of longer periods of fluc-
tuation - up to two minutes If a maximum lag of one tenth
the run length criterion were used.

The long period oscillation apparent in Runs 116 and
117 was not detected in the analysis because of the short
length of the run compared to the period of oscillation.
However, the use of run lengths long enough to ensure analy-
sis of such long periods would have been prohibitive in
terms of data storage requirements and, later, computer
analysis requirements. Since no information was available
beforehand to suggest the presence of long periods, run
lengths of 20 minutes were best suited to the purposes of
the experiment .

C. RECORDING OF DATA

Two tape recorders were used to record separate parameters
of simultaneous time series, a system not beneficial to
analysis due to the problem of tape synchronization during
reconstruction. Had a fourteen track tape recorder been

6H

available, all of the data could have been recorded simul-
taneously on one machine. As it was, the surface wave data
was recorded on a different tape from the one used to record
the pulse height and temperature data.

In preparation for digitization of the data, it was
discovered that on at least one of the dubbed tapes, the
pulse height data had exceeded the ±40$ deviation from the
carrier center frequency for the FM recording band and tape
speed used during the dubbing process. Attempts to reproduce
the data on a tape recorder other than the Sangamo were
unsuccessful due to the bandwidth limitation. Careful
testing of the Sangamo tape recorder, which was used to dub
the tapes, revealed that this machine was capable of handling
signals that exceeded the standard ±H0% deviation; in fact,
the discriminators proved to be linear out to at least ±60$
deviation from the center frequency. Had this tape recorder
not been designed to such broad specifications, much, and
perhaps all, of the pulse height data would have been
irretrievable due to an apparent operator oversight in
recording the data out of band.

D. PHASE II RUNS

The temperature microstructure activity during the runs
conducted in Phase II was generally higher than during the
Phase I runs. However, the acoustic pulse repetition rate
employed in Phase II precluded an analysis of the pulse
height time series by the digital methods used during this

65

thesis investigation. With a repetition rate of 3 Hz, a
pulse was transmitted every 333 milliseconds. Nominal travel
time from the projector to the hydrophones was 195 msec, after
which a pulse height was held by the sample and hold circuit
for 200 msec. Thus, the trigger signal that initiated a
pulse sequence arrived at the sample and hold circuit while
the previous pulse height was still being held. The result
was a distorted, two-step, pulse shape with the actual pulse
height not readily distinguishable from the effect of the
trigger arrival. A minimum pulse repetition interval not
less than the sum of the hold time (200 msec) and maximum
travel time would have precluded this problem.

E. REFLECTED SIGNALS

Calculated reflected path arrival times varied from
0.2 to 0.8 msec after the direct path arrival for the various
reflected paths. For the smallest time difference, 0.2
msec, only 7 cycles of the 35kHz direct path pulse would
have arrived before the reflected signal reached the hydro-
phone. Due to these considerations, the sample and hold
circuit was designed to require only five cycles to sense
and hold the signal. Thus, with the circuit operating
properly, no interference from reflected signals should
have occurred. However, surface reflected signals were
observed on Hydrophone 1 under certain circumstances (low
tide and 35 kHz frequency). This problem was alleviated
by a reduction in mast height.

GG

F. LOG KEEPING

Reconstruction of an experiment that was conducted one
year prior to analysis depended heavily on the comments
recorded in the logs. Scrupulous attention to detail in
original log-keeping made this effort relatively successful.
However, certain omissions occurred. These included lack
of weather data for a run, no notation of the acoustic
frequency used during a run, and inadvertent omission of
one run when transferring data from the rough log to smooth
log. This is the human factor in experimental work and
only constant care and cross-checking can minimize errors
such as these.

67

V. SUMMARY, RECOMMENDATIONS, CONCLUSIONS

The experiment conducted was unique for several reasons:

1) It involved simultaneous transmission along near-ortho-
gonal paths to investigate the degree of isotropy in acoustic
propagation.

2) Two acoustic frequencies were employed to investigate
the frequency dependence of the acoustic fluctuations.

3) A unique sample-and-hold device was designed and con-
structed to measure acoustic pulse heights without the need
for envelope detectors or recording of the pulse train.

4) A unique micro-scale temperature sensor system was
also designed and constructed to measure thermal microstruc-
ture .

5) The sensors were fixed to stable platforms, and were
remotely operated and monitored.

6) Multiple sensors were employed to investigate all
important aspects of the ocean environment.

7) Because of the fixed locations, experimental runs
were able to be conducted at various times of the year at
the same site.

The part of the experiment analyzed in this thesis repre-
sented only the initial stages of a project that has since
expanded and is still in operation. The fact that the pro-
ject was still in its embryonic development when these runs
were conducted resulted in several shortcomings which have

68

already been commented upon. However, it is felt that useful
information about the environment and its relation to the
acoustic propagation results presented herein can be gained
from implementation of the following recommendations:

1. Conduct an analysis of the temperature microstructure
data for the same runs as analyzed here. Comparison of the
results of spectral analysis may indicate the degree of
influence of surface wave activity on the microstructure.

2. Obtain the magnetic tape records for the surface wave
spectrum for similar analysis and comparison to the results
of acoustic and temperature analysis. Because of previously
noted problems with tape synchronization, this effort would
probably not prove conclusive.

For future experiments with purposes similar to this
one, it is suggested that:

1. Every effort be made to measure turbulent velocity,
temperature microstructure, surface waves, and acoustic
fluctuations simultaneously. It is imperative that all
sensors be maintained to accurately define the environmental
interactions .

2. All data be recorded on the same magnetic tape simul-
taneously to avoid problems with synchronization.

3. Vertical and horizontal thermistor arrays be employed
vice a single thermistor.

^1 . The geometry of the acoustic range be carefully
investigated with regard to the effect of reflected path
signals .

69

5. Equipment operating characteristics be well understood
to avoid difficulties such as those experienced in this
experiment with tape recording technique.

6. Vertical temperature profiles be included as a data
requirement .

7. Run length be modified as necessary to fully observe
the longest period fluctuations suspected to be present.

Conclusions from this analysis of the acoustic variabil-
ity are listed below:

1. The acoustic fluctuations were caused by variations
in the refractive index along with each propagation path.
These variations were most likely caused by the temperature
microstructure and by turbulent water particle velocity
resulting from surface waves. Whether the turbulent velocity
served solely as a mechanism for temperature distribution
and modification, or whether it also caused changes in

the refractive index by advecting other inhomogeneities ,
such as bubbles or sediment particulate, could not be deter-
mined from this analysis.

2. The fluctuations exhibited various degrees of anisotropy
with the propagation along the acoustic path oriented perpen-
dicular to the predominant swell direction generally subject
to greater variability.

3. No reliable trend was observed to indicate a significant
difference in variability due solely to the acoustic fre-
quencies used.

70

4. The possible influence of internal wave activity was
indicated by a long period fluctuation of the mean in at
least two runs .

71

APPENDIX A
Pulse Height Time Series and Analysis Results

This appendix contains two sections of figures. The
first section presents representative samples of the tempera-
ture microstructure activity present during each run. On
each sample, time increases to the right. Appropriate
scales and the qualitative classification are noted for
each figure .

The second section presents four plots for each of the
twelve runs analyzed. With two exceptions, the X and Y
scales for the same plot from different runs are identical
to aid comparison among runs. The first exception is for
Run 73 which was twice as long as any other; for this run
the X-scale of the time series and autocorrelation plots
has been modified and is defined on the plots. The other
exception applies to the Y-scale of the spectral energy
density plots. This scale varies slightly among the plots
due to the varying degree of fluctuations. The density
function values are acceptable for comparison among runs.

Reference to Tables I - IV is helpful in obtaining a
meaningful comparison among runs.

72

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LIST OF REFERENCES

1. Alexander, C.H., Sound Phase and Amplitude Fluctuations
in an Anisotropic Ocean, M.S. Thesis, Naval Postgraduate
School, Monterey, 1972.

2. Ash, D.E., Description of Operation, unpublished manu-
script, University of Auckland, New Zealand, 1972.

3. Barakos, P. A., The Effects of Internal Tides in Shallow
Water Acoustics, paper presented at The Eighty-Fourth
Meeting of the Acoustical Society of America, Miami
Beach, Florida, November 1972.

4. Bendat, J.S. and Piersol, A.G., Measurement and Analysis
of Random Data, Wiley, New York, 1966.

5. Bergmann, P.G., "Propagation of Radiation in a Medium
with Random Inhomogeneities" , Physical Review, v. 70,
p. 486-492, 1946.

6. Brownlee, L.R., Sound Propagation in an Inhomogeneous
Medium: The Sea - A Study and Measurement, M.S. Thesis,
University of Auckland, New Zealand, 1969 .

7. Campanella, S.J. and Favret, A.G., "Time Autocorrelation
of Sonic Pulses Propagated in a Random Medium," J .
Acoust. Soc. Amer., v. 46, p. 1234-1245, 1969 .

8. Crease, J., "Internal Waves", in Underwater Acoustics,
ed. V.M. Albers, p. 129-138, Plenum Press, New York,
1963.

9. Garrett, C. and Munk, W., "Oceanic Mixing by Breaking
Internal Waves", Deep-Sea Research, v. 19, p. 823-832,
1972.

10. Gregg, M.C. and Cox, C.S., "The Vertical Microstructure
of Temperature and Salinity", Deep-Sea Research, v. 19,
P. 355-376, 1972.

11. Gregg, M.C, Cox, C.S., and Hacker, P.W., "Vertical
Microstructure Measurements in the Central North
Pacific", J. Phys, Ocean, v. 3, p. 458-469, 1973-

12. Medwin, H., Sound Speed Dispersion and Fluctuations in
the Upper Ocean: Project BASS, Naval Postgraduate
School, Monterey, Report IIPS-6lMd73101A , 1973-

125

13. Mintzer, D. , "Wave Propagation in a Randomly Inhomo-
geneous Medium. I", J. Acoust . Soc . Amer., v. 25,

p. 922-927, 1953a.

14. Mintzer, D., "Wave Propagation in a Randomly Inhomo-
geneous Medium. II", J. Acoust. Soc. Amer., v. 25,
p. 1107-1111, 1953b.

15. Mintzer, D., "Wave Propagation in a Randomly Inhomo-
geneous Medium. Ill", J. Acoust. Soc. Amer., v. 26,
p. 186-190, 195*1 .

16. Morton, J. and Chapman, V.J., Rocky Shore Ecology of
the Leigh Area North Auckland, University of Auckland,
New Zealand, 1968.

17. Neal, V.T. and Neshyba, S., "Microstructure Anomalies
in the Arctic Ocean", J. Geophys. Research, v. 78,

p. 2695-2701, 1973.

18. Neshyba, S., Neal, V.T., and Denner, W., "Temperature
and Conductivity Measurements under Ice Island T-3",
J. Geophys. Research, v. 76, p. 8107-8120, 1971.

19. Raney, S.D., Procedures for Converting 7-Track Magnetic
Tapes to 9-Track Magnetic Tapes, informal report TN
0211-08 of W.R. Church Computer Center, Naval Post-
graduate School, Monterey, February 1973-

20. Sagar, F.H., "Fluctuations in Intensity of Short Pulses
of 14.5-kc Sound Received from a Source in the Sea",

J. Acoust. Soc. Amer., v. 27, p. 1092-1106, 1955.

21. Sagar, F.H., "Comparison of Experimental Underwater
Acoustic Intensities of Frequency 14.5 kc with Values
Computed for Selected Thermal Conditions in the Sea",
J. Acoust. Soc. Amer., v. 29, p. 9^8-965, 1957.

22. Sagar, F.H., "Acoustic Intensity Fluctuations and
Temperature Microstructure in the Sea", J. Acoust. Soc.
Amer. , v. 32, p. 112-121, i960.

23. Shoemaker, B.H., Interrelationship Between the Thermal
Microstructure, Internal Waves and Acoustic Propagation
in the Arctic Ocean, M.S. Thesis, Naval Postgraduate
School, Monterey, 1971.

24. Skudryzk, E.J., "Thermal Microstructure in the Sea and
Its Contribution to Sound Level Fluctuations", in
Underwater Acoustics, ed. V.M. Albers, p. 199-233,
Plenum Press, Mew York, 196 3 •

126

25. Stommel, H. and Federov, K.N., "Small Scale Structure
In Temperature and Salinity near Timor and Mindanao",
Tellus, v. 19, P. 306-325, 1967.

26. Taylor, F.J., Phytoplankton and Nutrients in the
Hauraki Gulf Approaches, unpublished manuscript,
University of Auckland, New Zealand, 1972.

27. Urick, R.J. and Searfoss, C.W., The Micro thermal
Structure of the Ocean near Key West, Florida: Part I -
Description, Naval Research Laboratory, Washington,
D.C., Report S-3392, 1948.

28. Urick, R.J. and Searfoss, C.W., The Microthermal
Structure of the Ocean near Key West, Florida: Part II -
Analysis, Naval Research Laboratory, Washington, D.C.,
Report S-3444, 1949.

29. Urick, R.J., Principles of Underwater Sound for Engineers,
McGraw-Hill, New York, 1967.

30. Woods, J.D. and Wiley, R.L., "Billow Turbulence and
Ocean Microstructure" , Deep-Sea Research, v. 19,

p. 87-121, 1972.

127

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Naval Postgraduate School

Monterey, California 939^0

4. Dr. Warren W. Denner 6
Director

Naval Arctic Research Laboratory
Barrow, Alaska 99723

5. Dr. Robert H. Bourke 1
Code 58Bf

Naval Postgraduate School
Monterey, California 939^0

6. Dr. Edward B. Thornton 1
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Naval Postgraduate School
Monterey, California 939^0

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Naval Postgraduate School
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128

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12. Dr. Robert E. Stevenson 1
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Scripps Institution of Oceanography
La Jolla, California 92037

13. Lt. Michael T. Korbet, USN 1
c/o 1930 Pendennis Drive

Annapolis, Maryland 21401

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129

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READ INSTRUCTIONS
BEFORE COMPLETING FORM

1. REPORT NUMBER

2. GOVT ACCESSION NO

3. RECIPIENT'S CATALOG NUMBER

4. TITLE (and Subtitle)

Shallow Water Acoustic Amplitude
Fluctuations at 35 and 65 KHz

S. TYPE OF REPORT 4 PERIOD COVERED

Master's Thesis;
March 1974

6. PERFORMING ORG. REPORT NUMBER

7. AUTHOR(«>

Michael Thomas Korbet

t. CONTRACT OR GRANT NUMBERS

9. PERFORMING ORGANIZATION NAME AND ADDRESS

Naval Postgraduate School
Monterey, California 93940

10. PROGRAM ELEMENT. PROJECT, TASK
AREA 4 WORK UNIT NUMBERS

I. CONTROLLING OFFICE NAME AND ADDRESS

Naval Postgraduate School
Monterey, California 93940

12. REPORT DATE

March 1974

13. NUMBER OF PAGES

131

14. MONITORING AGENCY NAME & ADDRESS!-// dlllerent from Controlling Office)

Naval Postgraduate School
Monterey, California 93940

IS. SECURITY CLASS, (of thlt report)

Unclassified

I5«. DECLASSIFI CATION/ DOWN GRADING
SCHEDULE

16. DISTRIBUTION STATEMENT (of this Report)

Approved for public release; distribution unlimited.

17. DISTRIBUTION STATEMENT (of the abttrect entered In Block 20, If different from Report)

IB. SUPPLEMENTARY NOTES

Research supported through contracts from
Naval Ordnance Systems Command (Code 03C)

19. KEY WORDS (Continue on reverie tide If necetttry and Identity by block number;

Underwater acoustics
Shallow water acoustics
Acoustic amplitude fluctuations
Temperature microstructure

20. ABSTRACT (Continue on reverie tide II necetttry and Idtnttty by block number)

An underwater acoustics experiment conducted in shallow water
(70 feet) off the New Zealand east coast in 1972-1973 is
described. Short acoustic pulses of 35 and 65 kHz sound were
projected along near-orthogonal paths of approximately 300 yards,
Environmental parameters were simultaneously observed.

Statistical and spectral analyses of pulse heights were
performed on 12 selected runs using digital techniques.

DD ,^73 1473
(Page l)

EOITION OF I NOV 65 IS OBSOLETE
S/N 0 102-014- 660 1 I

130

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(20. ABSTRACT continued)

Coefficients of variation ranged from 2.0$ to 15 - 5% - In almost
all cases, higher variability was observed along the acoustic
path oriented perpendicular to the predominant swell direction.
Along this same path, periods corresponding to common surface
swell periods were frequently evident in the autocorrelation
functions of the fluctuations. Coherence between the fluctuations
along each path was low, averaging about 0.1. Long period oscil-"'
lations suggestive of modulation by internal waves were apparent
in several runs. Mo significant dependence of variability on
acoustic frequency was detected.

Microscale temperature fluctuations measured simultaneously
are discussed.

DD Form 1473 (BACK)

1 Jan 73 . UIICI ASSTF1FP

S/N 01 02-014-()()(> 1 SECURITY CLASSIFICATION OF THIS PAGF.fH7..n O.r. F.nlmfd)

■i J 1 U b I

Thesis

K786 Korbet

am^f!l°Wwater acoustic
amplitude fluctuations
at J5 and 65 kHz.

151061

I Thesis
i;786
fc.l

Korbet .

Shallow water acoust-
amplitude fluctuations
at 35 and 65 kHz.

thesK786

Shallow water acoustic amplitude fluctua

3 2768 002 10491 1

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